CMSI 282
Homework #2

Submit, in hardcopy, answers to the following problems generated form LaTeX source according to the usual homework submission guidelines. Also build up your CVS repository with the following:

    /homework/cmsi282/hw2.tex
    /homework/cmsi282/src/main/java/edu/lmu/cs/yourloginname/sort/Bozosorter.java
    /homework/cmsi282/src/main/java/edu/lmu/cs/yourloginname/collections/PriorityQueue.java
    /homework/cmsi282/src/test/java/edu/lmu/cs/yourloginname/collections/PriorityQueueTest.java
    /homework/cmsi282/src/main/java/edu/lmu/cs/yourloginname/numbers/PrimalityTester.java
    /homework/cmsi282/src/test/java/edu/lmu/cs/yourloginname/numbers/PrimalityTesterTest.java
    /homework/cmsi282/src/main/java/edu/lmu/cs/yourloginname/crypto/AutoKeyVigenere.java
    /homework/cmsi282/src/test/java/edu/lmu/cs/yourloginname/crypto/AutoKeyVigenereTest.java

Make sure that you have run the setup-class script so that I can checkout and run your code from CVS while grading.

  1. Implement a Java class edu.lmu.cs.xxx.sort.Bozosorter (where xxx is your login name) with a single static method called sort whose job it is is to sort an array of integers using the Bozosort algorithm. Perform some empirical runtime studies on your method. That is, for list sizes of 2, 3, 4, 5, 6, ... (to as high as you want to go), give the average runtime of your method over several trial runs. Present your results in a nicely formatted LaTeX generated table.
  2. Implement a priority queue class with a heap implementation, and a unit test. Use Java or Groovy.
  3. Implement a Java class called PrimalityTester with a static method called isProbablePrime that takes in a value k and a BigInteger n and returns whether n is prime with a margin of error of 2-k using the Soloway-Strassen test. Write a unit tester that checks various values for k=40 (assume the primality test in java.lang.BigInteger is always correct).
  4. Implement the Autokey Vigenere cipher, from scratch, in Java. Treat characters as codepoints.
  5. The following ciphertext was intercepted. You know the message is in English and that the sender used a monoalphabetic substitution cipher. What is the plaintext? 
    UIQLDEVORHIWLTQTOKMQMWROUOQQMQLKIQWQVIEWRDQTLEQMWRWXFTWHTOA
DMRDQIOKWXMAOHMRMRHQVOQWLTAOMRQODPMDQWMRDQTLEQOEWAFLQITBVOQ
QWKWUIQLDEWREIRQTOQITOQVITWRIJFUOMRMRHQWVLAORSIMRHDBVOQBIBO
RQOEWAFLQITQWKW
  6. Decrypt the following ciphertext, given that you know it was encrypted with the bifid algorithm in which the Polybius square was laid out in the usual fashion using the keyphrase "Darn, not another cryptanalysis question". 
    TWBTLLAEPODTUBTWBTLTDLDDVSNNHEETLSKDDSIFGIIMWLYDKDDSPHBPQKOFHMDLSKRS
  7. If someone's RSA public key is (729880581317, 5), what is her private key? Give a detailed derivation, showing all work..